paper

The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation

arXiv:math-ph/0412044 · doi:10.1142/S0129055X0500242X

Abstract

We study the evolution of a quantum particle interacting with a random potential in the low density limit (Boltzmann-Grad). The phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation with collision kernel given by the full quantum scattering cross section.

74 pages, 4 figures, (Final version -- typos corrected)